There are currently three principal approaches to volumetric imaging in CT. In conventional volumetric CT, the object is scanned one slice at a time with a single row of detector elements and is translated only between slice acquisitions. In single-slice helical CT, the object is translated continuously while the x-ray tube rotates. The ratio of the object-translation distance per 360.degree. revolution of the source to the longitudinal width of the detector array is known as the pitch; it is usually chosen to be near 1. Finally, in multi-slice helical CT, the source illuminates several rows of detector elements at once in a small-angle cone-beam geometry. As in single-slice helical CT, the object is translated while the x-ray source rotates, although pitches much higher than 1 are feasible in this arrangement.
Helical CT offers a number of clinical benefits. The numerous advantages of helical CT have allowed it to displace conventional CT as the test of choice in many clinical situations and allowed for the development of new imaging protocols that were not even possible with conventional CT. Perhaps the most important advantage of helical CT is its high-volume-scanning speed. Helical CT can scan entire organ volumes in a single breathhold, thereby eliminating the acquisition gaps that can arise in conventional CT when anatomic structures do not realign precisely after breathing. Helical CT is thus particularly recommended for studies of the thorax, which suffers most from such respiratory motion and misregistration. Moreover, much thoracic imaging is performed with contrast agents, and the superior volume scanning speed of helical CT allows it to capture the phase of peak organ opacification, whereas conventional CT, if it can be used at all, will necessarily capture some slices only as the contrast agent dilutes. On this account, multi-slice helical CT provides clear advantages over even single-slice helical CT.
One contrast-enhanced study first made possible by helical CT is CT angiography (CTA), where the need for high temporal resolution is even greater than in organ contrast studies. Once again, multi-slice helical CT provides clear temporal resolution advantages over single-slice helical CT, but this is one area that could still benefit from improved temporal resolution. Faster scanning allows for more precise tracking of the injected bolus and thus allows for a shorter bolus to be used in the first place. This, in turn, reduces the chance that surrounding venous structures and perfused tissue will enhance before the scan is complete.
Additional clinical benefits of helical CT include its ability to perform retrospective overlapping slice reconstructions, which can facilitate nodule detection in the lung and liver. These studies in particular benefit from improved longitudinal resolution and reduced noise, which facilitate the detection of small lesions. Helical CT also makes possible the generation of multiplanar reformats from reconstructed volumes that do not contain any of the gaps and misalignments commonly found in conventional CT volumes, although these reformats would still benefit from improvements in resolution and noise isotropy.
There are a number of current approaches to longitudinal interpolation in helical CT. One group of these is referred to as the 180LI and 360LI approaches. Unlike conventional volumetric CT, which yields a complete set of projections for each slice being imaged, helical CT yields projections acquired at different longitudinal positions along the object. The general strategy for reconstructing slice images in helical CT is to interpolate the needed projection views from the measured projections. Helical CT reconstruction approaches differ primarily in their choice of interpolation approach and the amount of data used in the interpolation. In single-slice helical CT, most current approaches opt for linear interpolation. The simplest way of using the data is the 360LI approach, in which linear interpolation is applied to projections 360.degree. apart and located on either side of the slice in question. The 180LI approach exploits the redundancy of fan-beam data to generate a second helix of data prior to performing linear interpolation to obtain the desired projections.
Another approach involves the use of weighting functions. These interpolations can, of course, be performed in the straightforward way to yield transverse sinograms that can be reconstructed by fan-beam algorithms, but an alternative approach has been developed that provides a framework for more general and sophisticated strategies. The approach entails multiplying the measured helical projection data by a carefully designed weighting function prior to reconstruction by CBP. While naturally accommodating the 360LI and 180LI approaches, which in this context are known as full scan with interpolation and half-scan with interpolation, the strategy has spawned a number of other approaches, such as the underscan, half-scan, and helical extrapolative (HE) approaches.
Another approach involves the use of wide-kernels. In single-slice CT, approaches that use a wider interpolation kernel have been developed, such as an approach in which the interpolation weights minimize a worst-case normalized maximum error magnitude criterion. It was shown that this yields improved images over 360LI approaches, although Crawford and King later found little advantage to this approach over the 180LI and HE approaches. More recently, Hu and Shen introduced an approach incorporating longitudinal filtration into the weighting procedure, resulting in the use of more measured data in the estimation of each transverse sinogram. They did find advantages to this approach, particularly in the much greater flexibility it afforded for choosing the desired tradeoff between slice broadening and noise levels.
Other approaches have been developed for multi-slice helical CT. While also seeking to interpolate needed projection views from measured ones, multi-slice helical CT reconstruction must contend with the more complex sampling pattern of the measured projections in this geometry. A variety of interpolation strategies have been propose, many based on linear interpolation. It should be noted that whereas the small cone-beam angle encountered in multi-slice helical CT would seem to present an additional reconstruction challenge, existing approaches often disregard it because the longitudinal detector collimation (.about.2-10 mm) is very small compared to the source-to-detector distance (.about.1000 mm) and thus the cone angle is very small.
The physical characteristics of current approaches to longitudinal interpolation in helical CT must be considered. One of these characteristics is the aliasing and resolution properties of helical CT.
The physical characteristics of existing approaches to helical CT have been studied extensively. The longitudinal resolution of any volumetric CT reconstruction is naturally limited by the finite longitudinal collimation of the detector rows. Not surprisingly, the longitudinal interpolation step in helical CT leads to an additional broadening of slice profiles relative to conventional volumetric CT. However, there has long been a belief expressed in the literature that the ability to perform retrospective reconstruction at any longitudinal position offsets this broadening and, in fact, leads to longitudinal resolution superior to that in conventional volumetric CT. This belief has been bolstered by studies of SSP and MTF curves at the isocenter, performed with radially symmetric objects.
Yen et al. have clarified the situation by performing a detailed analysis of sampling patterns and aliasing effects in conventional and single-slice helical CT. They showed that a peculiar aliasing cancellation effect occurs only at the isocenter of a radially symmetric object, and that a fair comparison of helical and conventional CT and among different helical CT interpolation approaches should result in the examination of aliasing and resolution effects at other transverse positions. Indeed, according to their analysis, only at the isocenter is it even meaningful to speak in terms of continuous SSP and MTF curves that implicitly ignore the effects of aliasing. Such curves do, however, offer some measure of the transmission of principal, unaliased frequencies, and are thus still of some use for comparing different interpolation approaches in helical CT. For example, the superior SSP and MTF properties of the 180LI approach over the 360LI approach at the isocenter are reflected at other transverse positions by a decrease in the relative magnitude of the aliasing effect in the 180LI case. This ability to reduce the relative magnitude of aliasing effects will be referred to loosely as an improvement in longitudinal resolution, and improvements in longitudinal resolution that do not entail unacceptable increases in noise levels are always useful.
In an effort to improve resolution, some researchers have investigated the application of deconvolution to the reconstructed volume in order to compensate for the blurring introduced by the finite longitudinal collimation of the detector rows and the subsequent interpolation. Another desirable goal is to achieve more isotropic resolution, that is, to decrease the change in the relative magnitude of the aliasing effect as a function of transverse position and also to achieve comparable resolution longitudinally and transversely.
Noise properties are another consideration. The choice of interpolation approach also affects noise levels in the reconstructed volume, with approaches employing wiser interpolation kernels generally resulting in lower noise levels than those employing shorter interpolation kernels. Noise levels have been studied analytically and empirically by a number of investigators. Most significantly, Hsieh has examined the spatial distribution of noise levels in helical CT volumes reconstructed with linear interpolation approaches and found it to be non-stationary relative to that in conventional CT, a situation that can impede the detection of low-contrast lesions and lead to artifacts in MIP images. The nonstationarity of the noise has its root in the fact that the application of linear, and indeed most, interpolation approaches to samples corrupted by white noise leads to interpolated curves that have a nonstationary variance, with maxima at the points corresponding to measured samples and minima midway between such samples. Whereas Hsieh proposed a postprocessing approach to mitigate the appearance of the artifacts, an interpolation approach that eliminated the very source of the artifacts would clearly be desirable.
In addition to the possibility of artifacts, noise properties have important implications for patient dose, tube loading, and tube life. Specifically, a reconstruction approach that can reduce noise without significantly compromising accuracy allows scans to be acquired at lower tube currents, which reduces patient radiation exposure, allows for longer scans with fewer tube cooling delays, and extends tube life. Indeed, Hu and Shen have pointed out the benefits of approaches that allow noise levels to be controlled in more flexible ways than are allowed by approaches based on simple linear interpolation.
Other artifacts may also be present. Other artifacts that must be considered when one examines helical CT interpolation approaches include stair-step artifacts, partial-volume artifacts, and, in the multi-slice case, cone-beam artifacts. Stair-step artifacts can be seen in reformatted longitudinal slices containing inclined surfaces. The continuous boundaries of such artifacts take on a staircase appearance in these images. The origins of the artifacts and strategies for suppressing them were investigated in the context of linear interpolation approaches. Partial-volume artifacts in helical CT have the same origin as in conventional CT--the presence of significant axial variations in attenuation within a collimated beam--although helical CT provides some means for suppressing them. Cone-beam artifacts arise in multi-slice helical CT when techniques that ignore the small cone angle are used. These artifacts are seen principally around the spine and within blood vessels that have been fitted with stent-grafts. It is worthwhile to study the effect of any novel interpolation approach on these types of artifacts.
Finally, transverse reconstruction algorithms may be considered. Because the output of any helical CT interpolation procedure is a set of transverse fan-beam sinograms, the choice of reconstruction algorithm clearly affects the final image quality. Two principal approaches exist for fan-beam reconstruction. The first, direct CBP, involves convolving each projection with an appropriate filter, followed by a distance-dependent backprojection. This distance-dependent backprojection is computationally intensive and, it can be shown, liable to amplify noise and numerical errors in the outer regions of the reconstructed image, although it is generally very accurate in the central regions of the image. The second approach involves rebinning the fan-beam data into a parallel-beam sinogram and then employing parallel-beam filtered backprojection (FPB) to reconstruct the image. The rebinning entails a two-dimensional (2D) interpolation. While this approach is generally more efficient than direct CBP, the use of bilinear interpolation can compromise image accuracy. Accordingly, a need exists for an improved method of reconstructing CT images from helical CT data.